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Floating point is the binary analogue of scientific notation: internally it represents a number as a fraction and a binary exponent; the value is that fraction multiplied by the specified power of 2. (The C standard nominally permits other bases, but in GNU C the base is always 2.)
For instance, to represent 6, the fraction would be 0.75 and the exponent would be 3; together they stand for the value 0.75 * 23, meaning 0.75 * 8. The value 1.5 would use 0.75 as the fraction and 1 as the exponent. The value 0.75 would use 0.75 as the fraction and 0 as the exponent. The value 0.375 would use 0.75 as the fraction and -1 as the exponent.
These binary exponents are used by machine instructions. You can write a floating-point constant this way if you wish, using hexadecimal; but normally we write floating-point numbers in decimal (base 10). See Floating Constants.
C has three floating-point data types:
double“Double-precision” floating point, which uses 64 bits. This is the normal floating-point type, and modern computers normally do their floating-point computations in this type, or some wider type. Except when there is a special reason to do otherwise, this is the type to use for floating-point values.
float“Single-precision” floating point, which uses 32 bits. It is useful
for floating-point values stored in structures and arrays, to save
space when the full precision of double is not needed. In
addition, single-precision arithmetic is faster on some computers, and
occasionally that is useful. But not often—most programs don’t use
the type float.
C would be cleaner if float were the name of the type we
use for most floating-point values; however, for historical reasons,
that’s not so.
long double“Extended-precision” floating point is either 80-bit or 128-bit
precision, depending on the machine in use. On some machines, which
have no floating-point format wider than double, this is
equivalent to double.
Floating-point arithmetic raises many subtle issues. See Floating Point in Depth, for more information.
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